The discovery of neutrino oscillations have provided us with
convincing evidences for massive neutrinos and leptonic flavor
mixing with high degree of accuracy[1]}, [2]}, [3]}. The
understanding of the leptonic flavor structure is one of the major
open questions in particle physics. Several attempts have been
proposed to explain the origin of neutrino mass and the observed
pattern of leptonic mixing by introducing the flavor symmetries
within the framework of seesaw models[4]}. The flavor
symmetry often reduces the number of free parameters and leads to
the specific structures of fermion mass matrices including texture
zeros[5]}, [6]}, [7]}, [8]}, [9]}, hybrid textures[10]}, [11]}, zero trace[12]}, zero determinant[13]},
vanishing minors[14]}, [15]}, [16]}, two traceless
submatrices[17]}, equal elements or cofactors[18]}, inverse
hybrid textures[19]}. Among these models, the matrices with
texture or cofactor zeros are particularly interesting due to their
connections to the flavor symmetries. The phenomenological
examination of texture zeros or cofactor zeros in flavor basis have
been widely studies in Ref.[5]}, [6]}, [14]}, [15]}, [16]}
where the charged lepton mass matrices \(M_{l}\)  are diagonal.
However, no universal principle is required that the flavor basis is
necessary and the more general cases should be considered in no
diagonal \(M_{l}\)  basis. In this scenario, the lepton mass matrices
with texture zeros in both lepton mass \(M_{l}\)  and neutrino mass
matrix \(M_{\nu }\)  have been systematically investigated by many
authors[7]}, [8]}(for a review, see [9]}).
